Makeshift Measurements

Lesson

Grade:
3-5

Periods:
1

Standards:

Author:

Donna Coe

Location: unknown

There are many common objects that come in standard sizes. Students
will verify measurements for some of these objects, use these objects
to determine the size or spacing of other objects, and suggest
additional objects that can be included in the class’ list of
"makeshift measures."

Several days before the lesson, prepare the Measurement Task Cards.
In addition to the situations described on the cards, you may wish to
add some real life examples of your own. Copy the task cards onto heavy
paper, cut them apart, and put them in a container.

The day before using this lesson in class, display a few common
objects that come in standardized sizes. Possibilities include coins,
dollar bills, credit cards, envelopes, index cards, DVDs, baking pans,
and floor tiles. For the next day, ask students to bring in some common
items that are always the same size. For instance, you might
want to show them a standard letter envelope and say, "This is a
standard envelope. It measures 4‑1/8 inches by 9‑3/8 inches. In fact, every standard envelope measures this same size." Explain that you want them to bring in other objects that have this same property.

You may want to send a note home to parents explaining the
activity that students will be doing in class. Parents can help their
students find a few items that could be used.

Begin the lesson with students describing the objects that they
brought in, and have them share observations about the objects that
other students brought to class. As students share their thoughts,
emphasize the idea of size.

Ask students what they think today’s math lesson might be about,
given the objects that they have been discussing. When a student
suggests measurement, pass out rulers and direct students to find the
dimensions (length and width) of their items. Students should record
the name and measurements of each object on the Measurement Record Sheet.
Make sure that all students have some items in common to measure. For
instance, if some students brought in an index card, then distribute
index cards to the other students, too. That way, they will have some
items in common for later discussion.

After about 15 minutes, have students compare their data with
other students. This can be whole‑group sharing with the teacher or
students recording the information on a large chart, or it can be
partners working together to check each others’ work.

Assemble the whole class and tell students that everyone’s
measurements for the common items should be just about the same because
these objects (and others) come in standard sizes. At this time, check
to see if this is so. Have students explain and resolve any
discrepancies.

Explain the term standard size, and ask students why
they think these things come in a particular size. Students will
probably think of reasons that apply to their lives. Be sure to suggest
the following ideas if they don’t come up:

For convenience, all objects should be the same size.

Some items must work with other objects. For instance, a
standard envelope is made to hold a sheet of folded paper, so it needs
to be the correct size to do this.

Manufacturing is more economical if machines make large quantities of a few sizes rather than lots of different sizes.

Stores have limited display areas, and it’s easier to display
things that are the same size. Also, it’s easier to store items (in a
warehouse or store room, for example) that are the same size.

Ask students if they can think of any other common objects that come
in standard sizes. Chart the objects and their measurements. Additional
objects can be added as ideas arise.

Tell students that the mathematics people use most often are estimation and number sense.
That is, people usually deal with reasonable numbers, and they don’t
always need exact numbers. It also frequently happens that when someone
needs to measure an item, the appropriate tool is not handy. Ask
students to describe a situation when this might happen, and allow them
to offer suggestions. Possibilities might include:

Will a piece of furniture fit in the space available for it?

Is a frame large enough for a painting or photograph?

Will a gift fit into a gift box?

Will a rug be too big or too small for the floor it needs to cover?

Ask students to explain how they might handle each of the situations
they suggested. How could they get a good estimate if they didn’t have
a ruler, tape measure, or other measuring device? Students should
suggest that people could use items for which they know the size to
make an estimate. For example, most adults carry credit cards, their
driver’s license, and keys with them, and everyone always has their
fingers and their feet with them. A person might estimate the
dimensions of a floor by counting the number of floor tiles or by
walking heel-to-toe and then converting the result to inches or feet.

Refer to the chart of common objects from earlier in the
lesson. Take the rulers from students, and have them determine the
length of some items in the classroom, such as a pencil or the top of a
desk. On their own, students should realize that they can use the
reference items from the chart to make good approximations. For
instance, they might use a credit card to estimate the length of a
pencil. Remind students that estimation is important to this lesson, so
the computations can be approximate: "The pencil is roughly three
credit cards long, or about ten inches."

After students have estimated the lengths of several items,
discuss the results with the class. For each measurement, ask the class
to indicate if the answer is reasonable (thumbs up) or not reasonable
(thumbs down). Ask a few students to justify their answers.

Divide students into pairs. Put the Measurement Task Cards
in a bag or basket. Students should work together for the following
Think-Pair-Share activity. Carefully explain the following process
before students get started:

Partners will find a good place in the classroom to work together.

Pairs will pick one task card, and they will read the task out loud.

The teacher will signal the beginning of Think, which is one minute for students to individually ponder the problem and consider possible strategies for solving it.

The teacher will then signal the beginning of Pair,
during which partners have a conversation about ways to estimate the
length using common items. Students should understand that both partners should get a chance to share ideas during this five‑minute period.

The teacher will signal the beginning of Share, which can either be done as an entire group, or one pair of students can share with another pair.

You may wish to use non‑verbal signals such as a bell or other sound, a change in lighting, or American Sign Language for think, pair, and share.

Note that there are plenty of task cards. The cards can be
replaced in the container, and the activity can be repeated several
times.

The lesson can end with students sharing their ideas from
Think-Pair-Share, with all students completing the first Assessment
Option below, or with students writing an answer to one of the Key
Questions in their journals.

Have the students reflect upon their learning by doing a self assessment.

Three things I noticed during this lesson were…

Two things I wondered about during this lesson were…

One thing that could be added to our chart of referents is…

Ask students to consider other tasks that could be added to the set of Measurement Task Cards.
By presenting some of the student ideas to the class, this could lead
to an interesting discussion: "Here is another idea for a makeshift
measurement card. Do you think it’s a good one? Why or why not?" During
this discussion, do not mention student names. The discussion should
focus on the mathematics. Allow the author of the task card to modify
the task privately, if appropriate, after the discussion.

Students should select a classroom object and
determine its approximate size by using one of the makeshift
measures.The teacher should make note of each students’ skills. Does
she arrive at a reasonable answer? Did he select an appropriate item to
use? Does she use the reference object correctly? This assessment option can be done individually or in small groups while the rest of the class is engaged in another activity.

Extensions

Have students search for other objects that come in standard sizes
and add them to the chart. Students could do an online search at an
office store (such as Office Depot or Staples) to find common items.
Many office supplies are even called by their sizes, such as 10" × 13"
envelopes.

Have students pick a category of objects that come in
standard sizes (baking pans or sticky notes, for example). Create a
poster that could teach other students how to use them as makeshift
measures. Display the posters in the hallway or other visible spot in
the school.

Have students make wallet-sized reference card that
list the dimensions of some of the common objects. Give these cards to
friends and family.

Use common objects to estimate the area of objects, such as rugs, floor tiles, and game boards.

Students could research the story of the Smoot Bridge
at MIT. A student whose last name was Smoot had some friends measure
the length of a bridge by picking him up and laying him down across the
entire span. The project got so much recognition that they renamed the
bridge after him. Students could create a variation of this story that
uses themselves and their friends to find the length of an object of
their own choosing.

Questions for Students

1. Are your makeshift measures reasonable? How do you know?

[Students might justify their results using visualization (e.g., "I can
imaginethat the pencil is about as long as three credit cards"), or
comparison (they got a different answer than a friend.]

2. What other objects could be used to estimate measurements? Why would they be useful?

[Students could suggest many objects, such as a new pencil
("because there’s always one in my desk"), a bicycle ("because it stays
the same size and is easy to move"), or paper clips ("because they are
lightweight, of a standard size, and we have lots of them").]

3. Which is more useful as a referent, body parts or the objects we used today? Why?

[Students might suggest that either is more useful for
different reasons. For instance, they may say that body parts are more
useful, because you always have them with you, or they may say that
objects are more useful because their size stays the same. Either
answer could be correct, depending on the student’s justification.
Students should realize that the answer depends on the item being
measured and how accurate you have to be.

Teacher Reflection

How did students demonstrate understanding of the materials presented?

Was students’ level of enthusiasm/involvement high or low? Explain why.

How did you lesson address auditory, tactile, and visual learning styles?

What were some of the ways that the students illustrated that they were actively engaged in the learning process?

Learning Objectives

Students will:

Accurately measure dimensions of common objects collected by the teacher.

Use standard size objects as references to determine sizes or spacing of other objects.

Generate a list of additional objects that could be used as referents in measuring length.

My NCTM

Register Now

If you would like to rate this lesson, then please register. Riuscipisci bla feummod
olenim dignit irit luptatum zzriliquamet la commodigna facilit prat.